Uniform Loss Filters Valleys Through Velocity Contrast

Valley devices need a way to prepare states dominated by one valley before any downstream operation can use that degree of freedom. Existing routes usually rely on valley-selective sources, engineered geometries, external fields, or non-Hermitian designs that make one valley lifetime longer than the other. This paper argues for a simpler mechanism: keep the loss uniform, and let the intrinsic group-velocity difference between valleys convert equal lifetimes into unequal propagation lengths.

Core Contribution

That makes the proposal less dependent on a special source or lattice decoration than many valley filters. In the tight-binding graphene model, the authors use nearest-neighbor hopping, staggered onsite detuning, and a uniform imaginary term. With $t=1$, $m=0.2$, and $\gamma=0.1$, the calculated valley polarization approaches $\pm 1$ after about 50 lattice constants at $E=0.4$, and reversing the propagation direction flips the selected valley.

Technical Approach

The paper defines valley polarization as

where $W_K$ and $W_{K'}$ are the transmitted weights in the two valleys. In the acoustic implementation, the authors fabricate a triangular-lattice acoustic crystal with triangular scatterers, inject sound from either side, and map the pressure field over a large region. The measured real-space field is Fourier transformed to estimate valley weights inside regions around the two Brillouin-zone corners.

The experimental sample contains 100 unit cells along the propagation direction, and the pressure field is measured over a 75-unit-cell region. The usable acoustic frequency windows are 6476–6638 Hz and 8375–8500 Hz, where the lower and upper bulk modes have well-defined valleys. The paper focuses much of the quantitative decay analysis at 8420 Hz.

Figure 3 is the clearest experimental evidence for the mechanism. The intensity decay does not follow a single eigenmode curve because the source excites several modes, but the measured slope changes from an early-stage decay to a later-stage decay. The authors interpret this as the fast-decaying valley being washed out first, leaving the slower-decaying valley to dominate at longer distances.

Results and Analysis

The acoustic measurements support the central claim: valley selection appears after propagation rather than at injection. With left-side excitation, the measured polarization in the reported bands tends toward one valley; with right-side excitation, it flips sign, as expected from time-reversal symmetry and opposite propagation direction. The paper also reports that setting the sound speed to a real value in simulation removes the filtering behavior, which is an important control because it isolates background loss as the active non-Hermitian ingredient.

The most practically relevant caveat is signal attenuation. Loss-based filtering trades purity for transmitted intensity: the unwanted valley decays, but so does the useful signal. The authors estimate that when the valley polarization reaches -0.9, the signal-to-noise ratio remains around 28.8 dB. That is plausible for the acoustic experiment, but it is still a device-level trade-off rather than a free operation.

The paper then shows that the trade-off can be tuned. By deforming the triangular scatterers from an equilateral shape to an isosceles shape, with $h/d$ changed from $\sqrt{3}$ to 2.4 while keeping the triangle area at 92.932 mm², the authors increase the group-velocity contrast without changing the working frequency. In the reported comparison, the deformed sample reaches -0.9 polarization at a longer distance than the original sample but with higher remaining sound intensity.

The end matter extends the same argument to uniform gain. Flipping the sign of the imaginary frequency part changes attenuation into amplification while preserving the velocity-contrast mechanism; at 8420 Hz, the plotted gain case reaches 0.9 valley polarization with about 45.62 dB intensity. This is a useful theoretical control, but it is not the same level of evidence as the fabricated dissipative acoustic device.

Limitations

The strongest results are in one acoustic platform, with photonic and electronic versions left to supplemental design rather than experimental realization. The method also requires a group-velocity contrast between the valley modes; uniform loss alone is not sufficient. Finally, the filtering length and signal level are coupled, so applications that need compact devices or high transmitted power will have to tune geometry, loss, or gain rather than directly adopting the demonstrated sample.